Monday, March 29, 2010

It's been twenty-eight days now since they arrived. At first we thought they were friendly. It was the Lie groups at first: SO(3) appeared in the sky above Chelmsford, and GL(3,R) blocked the P&O ferry at Rotterdam. The experts said it would stop with the Lie groups, but it didn't. Two days later the vector spaces started appearing, and the day after that it was the differential manifolds. A cornucopia of mathematical objects erupted into the material world.

It was a shock, but, you know, life goes on. People still went to work each morning. Commuters on the M25 zig-zagged around a Hilbert space which was dangling a closed subspace onto the middle lane; transatlantic flights were diverted to Southampton and Bristol when a particularly large non-distributive lattice appeared over Terminal 5 at Heathrow; and the Chelsea v Man United match had to be postponed when a non-commutative C*-algebra touched down at Stamford Bridge.

The mathematical objects appeared at first to be just as inert as they were inscrutable. Some hawkish military types suggested we fire battlefield lasers at them, but, as a strategy, this seemed to rather neglect the fact that the targets in question were abstract, and as such, were invulnerable to assault by packets of mass-energy.

We all got the feeling, however, that we were being watched. Assessed. After ten days, they launched phase two: a firestorm engulfed Swindon on a Wednesday afternoon; the Angel of the North melted like butter in a microwave; and seventy-two telecommunication managers vomited spinal fluid over their PAs. Tectonic tremors shook the major cities of the world. The Earth's magnetic field began to madly gyrate across the globe, green auroral curtains shimmering in the night-sky at equatorial latitudes. Extinct volcanoes lumbered into bellicose life, emetically disgorging viscid flows of lethal magma. And when the Earthquakes and tsunamis came, civilization disintegrated.

I don't know how many of us there are left. We hide in subterranean tunnels and catacombs, where they find it difficult to locate us. We're running out of food and fuel. We have no ammunition which has any effect on them, and we don't understand their motives or capabilities. If you find this message, it's probably already too late.

Sunday, March 28, 2010

There was a poignant moment in the paddock at the Hungaroring on the Friday afternoon. A flood of photographers and television journalists swept across from the grandly titled McLaren brand centre and surrounded Lewis Hamilton as he strode purposefully towards the team garage.

In the crush, nobody noticed Jenson Button as he ducked and weaved a path through the seething mass of humanity, the winner of last year's race here alone and unacknowledged by the jostling onlookers. It was a stern reminder of just how relentless, unforgiving and hard-edged the F1 business can be when it comes to consuming the careers of the vulnerable. (Alan Henry, Autocourse 2007-2008, p25).

By lap 6 of today's Australian Grand Prix, Lewis Hamilton had already passed his McLaren team-mate Jenson Button. Thereafter, however, their courses diverged, to the extent that Button won the race and Hamilton trailed in sixth. Understanding the root causes of this divergence will be crucial in determining whether this was merely a one-off, or the harbinger of a pattern to be repeated throughout the season.

Button's victory was clearly built upon his early decision to swap to slick tyres on a still-damp track surface, and this decision was only available to Jenson because of his extreme sensitivity to the amount of grip available in such circumstances. This is a sensitivity denied even to Hamilton, so Lewis immediately found himself a number of places behind Button after his own pit-stop a couple of laps later.

Nevertheless, this was still a race that Hamilton could have won, for he then mounted a stirring charge, passing cars left, right and centre, until he became momentarily becalmed behind Kubica's second-placed Renault. At this stage, McLaren then instructed Hamilton to make a second pit-stop for tyres, a decision which cost him any prospect of a decent finishing position.

So was this decision really the crass tactical blunder that Lewis was suggesting it was by the end of the afternoon? Whilst Button was able to make his solitary set of slick tyres last for the remainder of the race, Jenson has a smoother driving style than Lewis, and his superior track-position meant that he was asking less of his tyres than Hamilton. If Hamilton's tyres genuinely wouldn't have survived the race, then this is an unfortunate omen for the rest of his season.

Lewis, however, has claimed that his tyres were "great" at the time he pitted, so the alternative possibility is that McLaren made yet another bizarrely ill-judged strategy call, comparable to China 2007 or Germany 2008. If so, then it is perhaps time for Lewis to finally take control of such strategy decisions, and veto any recommendations from the team which seem so counter-intuitive.

Either way, Lewis Hamilton will come away from the Australian Grand Prix weekend with plenty of food for thought.

Saturday, March 27, 2010

At some time in 1992, whilst at the wheel of a Volkswagen Passat Estate, I was attempting to move away from a set of traffic lights at Cemetery Junction in Reading, when I inadvertently applied too many revs, and engaged the clutch a little too rapidly. As a consequence, the car briefly broke traction, an anti-social practice I now know to be referred to as hooning.

I was driving in an over-exuberant manner. What I did was silly, and I want to apologise for it.

Tuesday, March 23, 2010

"I believe that our start to the season has been mostly encouraging. Our race pace in Bahrain looked respectable – we had the fastest car for much of the second half of the race." (Martin Whitmarsh, McLaren F1 Team Principal).

"The Red Bull is ridiculously faster than anyone else's car. It's insane. The downforce they had on their car last year was at some points just about double what we had. They have both got the fastest car by quite a big step. They should be quite a lot further ahead in general." (Lewis Hamilton, McLaren F1 driver).

Here's an interesting development. Contrary to the optimistic noises being made after raceday in Bahrain, McLaren F1 driver Lewis Hamilton has suggested that Red Bull are way ahead of the field this year. He claims that Red Bull had "double" the downforce of McLaren at times last year, and that even Ferrari are a good half-second behind the Red Bull pace this year.

These claims, however, don't really bear up to analysis. For example, the peak downforce of an F1 car is about 1200kg, and an extra 5% of downforce (60kg) will be rewarded with a half-second improvement in lap-time. Even allowing for the fact that McLaren were initially more than two seconds off the pace of the Red Bull in 2009, and even allowing for the fact that lap-time improvement will not be a linear function of downforce, Red Bull would not have had double the downforce of the McLaren at any stage last year. If nothing else, that would amount to an extra 1200kg in terms of peak downforce, (i.e. over a tonne!).

Secondly, the Red Bull of Sebastian Vettel only out-qualified the Ferrari of Massa by 0.1s in Bahrain. In the race, Vettel pulled away from the Ferraris at the rate of about 0.3s a lap on the soft tyres, but was then pegged back on the harder tyres. It's difficult to see where an advantage of 0.5s a lap comes from.

Hamilton must know that his statement about the respective downforce levels of the McLaren and Red Bull is strictly inaccurate, so what lies behind this hyperbole? It's always possible that this was just an off-the-cuff series of comments, but coming a matter of weeks after relieving his own father of management responsibilities, it may be that Hamilton is making a foray into Formula One full-spectrum warfare. In other words, Hamilton's statement may have been designed to achieve some political effect, both inside and outside the team.

For a start, McLaren, in Hamilton's judgement, may simply be needing a rocket up the backside. In addition, Red Bull's engine supplier, Renault, appear to be on the verge of receiving permission from the governing body to effectively improve the performance of their engine, and the FIA have also just closed a loophole in the diffuser regulations which McLaren, amongst others, were exploiting. Thus, Lewis may feel it necessary to exaggerate the scale of Red Bull's technical advantage in order to elicit more favourable subsequent treatment from the governing body.

It'll be interesting to see if Lewis came make the transition to a full-scale political operative, in the style patented by Herr Schumacher...

Saturday, March 20, 2010

The setting Sun cast a baleful glare across the riven countryside of Treviso, northern Italy. Beneath the cockpit of Francesco Barraca's SPAD VII biplane, the landscape scrolled like a papier-mache diorama, the trenches thrown into deep shadow, and a shimmering amber glow reflecting from the waters of the River Piave as it curled around the base of Montello hill.

A conduit for pure alpine meltwater, flowing to its Venetian outlet on the Adriatic, the Piave now cut its way between fields of war, and formed the front to which the Italian forces had retreated after their 1917 defeat at Caporetto. Montello hill, a moraine deposited in the landscape by an ancient glacier, provided a stronghold for the Italians as the Austrians gathered their forces, and launched an attack across the Piave on the 15th June 1918.

On the 19th, the Italians staged a counter-attack, and that evening, Italy's number one fighter pilot, with 34 victories to his name, took to the skies to strafe the Austrian positions from above.

As Barraca placed his biplane into a shallow dive, he fettled the Vickers machine-gun sitting atop the engine cowling, and prepared to open fire. Swooping low across the Austrian lines, he heard a sudden polyphonic whistle to one side, followed instantly by a volley of bullets tearing a line of holes across the metal cowling. Immediately, orange flames were licking around the base of the fuselage. Barraca jettisoned the fuel tank, but the conflagration spread in seconds to the canvas wings. Maggiore Francesco Barraca was now fighting for his life, frantically banking the plane towards Montello, seeking a site for the inevitable crash-landing.

Montello, however, was heavily forested. As Barraca fought with the rudder, his vision was obscured by smoke billowing from the nose, and he clipped the top of a chestnut tree, ripping the undercarriage away, and pitching the fuselage forward into a final short dive. In a small clearing between the trees, the biplane hit the ground with a sickening thump that ripped the final breath from the V8 Hispano-Suiza engine, and sent the frame of Barraca's mount cartwheeling towards a copse of oak trees.

Shrouded in smoke and flame, Barraca's shattered bones lay entangled in the splintered frame of the biplane, scarlet blood mixing with jet black engine oil. Still conscious, Barraca heard the sound of Austrian soldiers approaching, calmly loaded his pistol, and fired a single shot into his skull. When the soldiers extinguished the fire, and reached Barraca, the only part of the aircraft frame which remained untouched by the flames, was Barraca's insignia: a prancing black horse...

Friday, March 19, 2010

"It is verging on the ridiculous to be worried about them." Richard Wakefield from Manchester University's Dalton Nuclear Institute, quoted in the Guardian. As major UK airports roll out the use of full-body scanners in the war against would-be plane bombers, Wakefield says that the dose of radiation from them - about 0.02 mSv per scan - will pose no risk to travellers. (Physics World, March 2010).

Holy mother of all that's radiologically moly! 0.02 millisievert per scan? That's 20 microsieverts! The UK limit on ionising radiation doses to the public (excluding medical radiography) is 1 millisievert (1 mSv) per annum, and at 20 microsievert per scan, you'd only need to pass through a scanner on the outward and inward legs of 25 flights per annum to breach this limit.

One's thoughts immediately turn to the nomadic denizens of the UK's Formula One community, who already receive an annual cosmic-ray dose which could be as high as 2 mSv per annum, (assuming a pessimistic dose-rate of 10 microsievert per hour at commercial jet altitudes).

Fortunately for Mr Ecclestone's plucky flying circus, a perusal of the original article in The Guardian reveals that the dose from a certain type of airport scanner is actually just 0.02 micro­sieverts, not 0.02 millisieverts. It seems that in this case, at least, The Guardian is able to transcribe scientific information more reliably than Physics World.

Except, that is, for one further problem. There is no radiation expert at Manchester University's Dalton Nuclear Institute called Richard Wakefield. There is, however, one called Richard Wakeford. The erroneous spelling seems to originate from The Guardian article, and to have been transcribed, without verification, into Physics World.

The Health Protection Agency report that "even in the case of frequent fliers the doses are unlikely to exceed 20 micro Sv/year." Moreover, these doses of ionising radiation only arise from scanners which use x-ray backscatter techniques. Terahertz scanners, in contrast, and by definition, use non-ionising radiation.

There was plenty of time during last Sunday's Bahrain Grand Prix to analyse the spacing of the palm trees at the Sakhir circuit, and to conclude that they possess an unnatural uniform spacing, in stark contrast to the Poisson clustering of real trees. Hence, for those running up junior jet-club miles en route to such exotic Formula One destinations, the greatest risk to health this year may come not from ionising radiation, but from the possibility of being bored to death.

Monday, March 15, 2010

"For the process philosopher, the classical principle operari sequitur esse (functioning follows upon being) is reversed: his motto is esse sequitur operari, since being follows from operation." (Nicholas Rescher, Process Philosophy, A Companion to Metaphysics, p417)

Hollywood actress Anne Hathaway, has recently been puzzling newspaper columnists with her pronouncements on physics and philosophy. In early 2009, Miss Hathaway could be found extolling the virtues of process metaphysics at one of the film industry's increasingly rare awards ceremonies. Just over a year later, the erstwhile star of The Princess Diaries, admitted to GQ magazine that her intellectual interests included a voracious appetite for physics:

"I'm interested in elementary particles. What I like thinking about is how time and space exist in the universe and how we understand it.

"Any spare time I have, I bury my head in a physics textbook. I'm learning. I'm reading a lot about Einstein. I like theories. I want to understand string theory. I am dying for someone to explain quarks to me!"

To most newspaper journalists, these separate statements might appear logically unconnected, and perhaps even a little contrived. It may be, however, that Anne has simply been reading some of philosopher Nicholas Rescher's output. For those unfamiliar with process philosophy, the basic idea is that processes should be treated as more fundamental than objects; processes, it is claimed, are basic, whilst things are derivative. Now, Rescher in particular claims that this process philosophy finds support within modern quantum physics:

"Matter in the small, as contemporary physics concerns it, is not a Rutherfordian planetary system of particle-like objects, but a collection of fluctuating processes organized into stable structures...Twentieth-century physics has thus turned the tables on classical atomism. Instead of very small things (atoms) combining to produce standard processes (windstorms and such) modern physics envisions very small processes (quantum phenomena) combining to produce standard things (ordinary macroscopic objects) as a result of their modus operandi," (ibid, p418).

Hence Miss Hathaway's interest in quarks.

On a point of substance, however, one might disagree with Rescher's sentiments. Process philosophy finds no more support or refutation in quantum physics than it receives in classical physics. The ontology of both classical physics and quantum physics reflects the common dichotomy between things and processes. In quantum physics, there are different types of quantum fields, and these fields have excitation states which are colloquially referred to as particles. These particles are exhaustively classified by the values they possess for properties such as mass, spin and charge. These properties determine what type of mathematical object the particles are represented by, and which type of evolution equation those objects must satisfy. Quarks and electrons, for example, are spin 1/2 particles with a non-zero mass, they are represented by cross-sections of Dirac spinor bundles, and their evolutionary processes are such that those cross-sections must satisfy the Dirac equation. There are both objects and processes in quantum physics, just as there are objects and processes in classical physics.

Friday, March 12, 2010

Late winter in deciduous woodland. The air is damp, the light is flat, the trees remain stark and skeletal.

Here, in a lichen-laden copse, stand a Husband-and-Wife, permanently rooted to the spot. Initially two separate trees, with separate boles on either side of a small rivulet, and presumably with separate root systems, they have joined together in dendrological wedlock at a height of about 20 feet.

A branch from one appears to have naturally grafted itself onto the main trunk of the other, a type of woody kiss called inosculation. Whilst such H-trees can be artificially encouraged, their spontaneous formation is a touchingly rare piece of dendro-topology.

In fact, alphabetic topology seems to be very much the order of the day, with McLaren's new F-duct causing something of a stir at the first race of the 2010 Formula One season, in Bahrain. It transpires that the air entering this duct flows into the cockpit, from whence it somehow influences the flow feeding the rear wing, and in a manner which can be controlled by the driver.

Perhaps there is a pipe leading from the F-duct into the driver's rectum, from which point the air flows up through the gastro-intestinal tract of our gallant pilote, out of his helmet, and thence on to the rear wing. The driver is thereby able to stall the wing, and reduce drag down the straights, by the simple expedient of relaxing his lower jaw. However, he does then have to remember to keep his mouth shut in the corners, as well as in the press conferences.

Wednesday, March 10, 2010

It is August 1930, and Tazio Nuvolari has journeyed with Alfa Romeo designer, Vittorio Jano, to Vienna after contesting the Linthal-Klausenpass hillclimb. Here, within the Ringstrasse, lies the intellectual and cultural hub of the city: a network of elegant coffee-shops, furnished with marble-topped tables, in which patrons are provided with newspapers, reference books, writing materials, and the atmosphere to discuss and develop the pressing political and philosophical issues of the day.

Within the Cafe Griensteidl sits the young Viennese logician Kurt Godel, an untouched glass of water before him on the tabletop. Wiry and bespectacled, his head tilts down towards the glass, and a permanent frown appears to crease his brow. Across the table sit Jano and Nuvolari, each nurturing a cup of coffee.

The introductions complete, and the small-talk exhausted, a brief silence plays over the background noise, (a cacophonous and symphonous medley of chatter in the coffee-shop, merging melodiously with the sound of a distant waltz, and the vaporous exhalations of a locomotive surging out of Westbahnhof station).

"Signor Nuvolari, please tell me about what you understand by the concept of the limit," asks Godel, without lifting his head.

Nuvolari exchanges a wary glance with Jano. "The limit? Well, suppose I begin driving at a certain speed, and judge that I am a certain distance from the limit of a vehicle's adhesion. I can divide that distance in half, and take myself to that midpoint. I am then going faster, yet I have still not reached the limit of the vehicle. I can then take the new distance that separates me from the limit, divide it in half again, take myself to that next level, and so on, ad infinitum, going faster every time, but never actually reaching the limit of the vehicle. That is what I understand by the limit: it is the boundary of my performance; it restricts me, yet I play with it and manipulate it, see it and feel it, but I can never attain it."

"I see," says Godel. "The possibility of infinite perfectibility within a finite limit interests me. But how do you know this limit is there, if you never attain it?"

"By exceeding it," replies Nuvolari flatly.

Godel finally raises his head, and stares unblinkingly at Tazio. "Vienna is the home of the unconscious, Signor Nuvolari. How much do you think you know about yourself when you're driving?"

"I know that there are things about myself as a racing driver which I could never know, if that's what you mean? If I knew everything there is to know about myself, then I would need to know that knowledge in turn, and then I would need to know that I know that knowledge, ad infinitum. Hence, I would never be able to know myself completely without being infinite."

"Quite," replies Godel with a wry smile.

In September 1930, Godel will go on to raise the possibility at a conference in Konigsberg that there are logically true propositions which cannot be proven. In 1931, he will publish his incompleteness theorems, thereby destroying the 'formalist' programme which sought to establish that all mathematical truth could be obtained by applying syntactical rules of deduction to axiomatic systems. Godel and Nuvolari, however, will never meet again.

Saturday, March 06, 2010

"The strategy I am advocating is that physics, in becoming more or less completely aligned to mathematics (in terms of content, at least), will be able to penetrate down the ladder of explanation to the very deepest rung of all: existence."

Philosopher of Physics Dean Rickles has an interesting paper which proposes an explanation for why there is something rather than nothing. Rickles submitted his article, On Explaining Existence, to a recent essay contest organised by the Foundational Questions Institute. The resolution he proposes is simply that the physical world is identical to the mathematical world, hence the existence of the physical world is necessary rather than contingent:

"Either existence is contingent or it is necessary. If it is contingent then there is no complete coherent account of existence. If it is necessary then we need a necessary structure to ground this fact. Mathematical structures are of this kind. If reality is mathematical then it must exist. Reality is mathematical (as evidenced by the effectiveness of mathematics in the sciences). Therefore, there is existence. This is not a case of logic 'causing’ existence, or bringing existence into being 'out of nothing’. Mathematical structures are timeless. We can add to this the fact that if this is the only reason that can be found for existence to be the case, then physical reality (or just reality) has to be mathematical. In other words, the universe is mathematical because there is existence, and the only reason for there to be existence is that there are mathematical truths."

Martin Heidegger claimed that this is the most important question in philosophy. Here I wish to focus on a special case of this question, namely: 'Why is there something physical rather than nothing physical?' The implicit assumption which underlies this question is that the existence of the physical universe is contingent. If one rejects this assumption, then one possible answer to the question is that the physical universe exists necessarily. Mathematical structures exist necessarily because mathematical existence is merely absence from contradiction, and modern theoretical physics represents the physical universe as a mathematical structure, hence the physical universe exists necessarily as a special case of mathematical existence.

Rickles also makes the following excellent point about Godel's theorem:

"The theorem does not tell us that there is any problem with mathematical truths per se; only that there is no algorithmic way of generating all such truths. The mathematical universe is safe from Godel’s theorem. We must distinguish between truth and provability."

Elsewhere, however, Rickles comments that "Godel’s theorem would surely bite: for a theory will be a representation and any such mapping will be lossy," and on this point I don't totally agree. It is important to emphasise the distinction between theories and models which exists in mathematical logic, and to reiterate the point made in my 2009 post, Theories of Everything and Godel's theorem, that "whilst the theory of a model, Th(M), may be undecidable, it is guaranteed to be complete, and it is the models of a theory which purport to represent physical reality." The theory of our universe's mathematical structure is guaranteed to be complete and consistent, even if it might transpire to be undecidable, and this is far from 'lossy'.

Monday, March 01, 2010

"I definitely felt God's presence with me when I was a driver. When I was young I even tried to use God to help in my career. That was a mistake because even though He helped me a lot, He delivered a lot of bad accidents." (Alex Dias Ribeiro, Overdrive, p176.)

Philosopher Thomas Nagel famously argued that consciousness is defined by the fact that there is something which it is like to be the subject of experience: "An organism has conscious mental states if and only if there is something that it is like to be that organism — something it is like for the organism," (What is it Like to Be a Bat? 1974, p436). Ineluctably, it follows that there is also something which it is like to be a racing driver.

Overdrive, by the pseudonymous 'Clyde Brolin', is first and foremost a book about what it is like to be a racing driver in the Zone. In this state of mind, a driver attains mental clarity, he feels at one with his car, and driving fast at the very limit becomes effortless. Accessing this mental state requires the relaxation of the conscious mind, permitting the subconscious to take control. Under these conditions, the consciousness of the driver is able to sit back and observe, from an almost disinterested perspective, the actions of his own body.

The effectiveness of this state of mind, not just in motor racing, but in all sports and high-performance physical activities, is perhaps unsurprising. Estimates of the amount of information stored in the brain, and the manner of its storage, vary, but one set of calculations suggests that whilst the brain can store somewhere between 1010 and 1015 bits of information, the amount of information which can be consciously held at the forefront of the mind, is only between 1 and 10 million bits, a quantity of information comparable to that coded in a single book, (The Anthropic Cosmological Principle, Barrow and Tipler, p136-137). Hence, it is the interplay between the consciously held information and the far greater quantity of subconscious information, which holds the key to sporting performance.

As Brolin explains, many drivers in the Zone also have the ability to slow down the subjective flow of time. This capability is common amongst all sportsmen, and can also be experienced outside sport in moments of great danger, such as the fractions of a second just before a car crash. It is a phenomenon which has attracted the interest of various scientists, and two possible explanations for the stretching of subjective time have been proposed: it could be due to an acceleration in some neurophysiological clock, or it could be a trick of memory. Neuroscientist David Eagleman, of Baylor College of Medicine in Houston, Texas, for example, has conducted experiments which lead him to believe the latter:

An intense experience, with heightened fear or excitement, rivets our attention and evokes the firing of many neurons across the brain...causing us to soak up more sensory details...Richer memories seem to last longer...because you assume you would have needed more time to record so many details..."You lay down denser memory [claims Eagleman]. When you read it back out, you think 'Gee, that was taking a long time'."

Yet Brolin suggests that racing drivers are not only able to stretch time when they are in the Zone, but many are also subject to Out-of-Body Experiences (OBEs). The most famous cited incidence of this occurred to Ayrton Senna in practice for the Monaco Grand Prix in 1988: "Suddenly I realised that I was no longer driving the car consciously. I was kind of driving by instinct, only I was in a different dimension. I was way over the limit, but still I was able to find even more. It frightened me because I realised I was well beyond my conscious understanding."

Such experiences go well beyond the transfer of control to the subconscious; rather, they involve a loss of self-identity, and a weakening of the sense that one's spatial location is fixed somewhere just behind the eyes. Nevertheless, scientists believe Out-of-Body Experiences have a rational explanation, and one reason for this is that pharmaceutical products, such as ketamine, are known to induce very similar mental states. Such chemicals merely change the physiological state of the brain, hence if OBEs can be induced by chemical products, it follows that such experiences can be explained in neurophysiological terms.

Various religious rituals have also long been known to induce such mental states, and this has attracted the interest of researchers such as Andrew Newberg, a neuroscientist at the University of Pennsylvania in Philadelphia. The parietal lobe in the brain is thought to be at least partially responsible for the conscious sense of self and spatial location, and brain scans conducted on religious devotees engaged in meditation, suggest that the parietal lobe temporarily shuts downs in such experiences:

"Broadly speaking, the left-hemisphere side of this region deals with the individual's sense of their own body image, while its right-hemisphere equivalent handles its context — the space and time inhabited by the self...When you look at people in meditation, they really do turn off their sensations to the outside world. Sights and sounds don't disturb them any more. That may be why the parietal lobe gets no input," says Newberg. Deprived of their usual grist, these regions no longer function normally, and the person feels the boundary between self and other begin to dissolve. And as the spatial and temporal context also disappears, the person feels a sense of infinite space and eternity.

The really mysterious thing about Brolin's book, is that despite ten years' worth of research, there is no mention, not even in passing, of such scientific research. In fact, the reader could almost gain the impression that no such research exists. Moreover, Brolin makes a frequent point of claiming that there is no rational, logical explanation for the experiences of racing drivers in the Zone:

"By pushing to the limit and beyond [Senna] found standard rational explanations no longer sufficed," (p12); "our vocabulary becomes deficient outside the range of the purely logical and tangible," (p19); "few could come up with a rational explanation for what happens at these 'peak' moments," (p23); "What drivers go through at these special times thus defies all logic. So is it beyond the scope of rational thought to bend time from the confines of the cockpit?" (p117); "This is an indication of the untapped potential held within our subconscious, but quite how it happens remains beyond simplistic logical explanation," (p120); "logic and rationality begin to stumble when you start seeing without using your eyes," (p140); "Some of the worldly wizardry described in these pages defies rational explanation," (p186); "Looking into the future may sound beyond the bounds of rational explanation," (p193); "They go beyond to new heights where rational language cannot suffice," (p227).

The author is putting an awful lot of effort into trying to convince the reader that there are things beyond rational explanation, and this seems to be crucial to the overall philosophical development of the book. Brolin begins with the testimonies of racing drivers who have been in the Zone, and then infers from these testimonies that such drivers have experienced something spiritual. From the spiritual, he then segues into the religious. And, by the final chapters of the book, we have drifted quite a distance from the Zone, and quite overtly into the accounts given by various sportsmen of their 'relationship with God'. Eventually, we are told that the Zone is a "gateway to the divine," (p157), and that "the Zone is one indication that we are all linked to the same source," (p228).

However, whilst the book suffers from this philosophical flaw, it is still a unique and fabulous work. The author has extracted a gripping and fascinating collection of lucid recollections from many of the most famous names in motorsport. Brolin has essentially unearthed a whole world of private experience which has received little prior attention. The accounts rendered of being in the Zone should be treated as a treasure-trove for psychologists and neuroscientists, and even the more overtly religious testimonies later in the book can be seen as an interesting anthropological study of the beliefs held by certain modern tribes. Buy it!